Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. this statement implies that the masses of the two stars are equal (see figure below). assume the orbital speed of each star is |v with arrow| = 160 km/s and the orbital period of each is 13.7 days. find the mass m of each star. (for comparison, the mass of our sun is 1.99 1030 kg.)

 M = 4.61 10³¹ kg

Explanation:

For this exercise we will use Newton's Second Law where the force is the gravitational outside

       F = ma

       G M₁ M₂ / r² = m a

The acceleration is centripetal

       a = v² / r’

Let's replace

The mass of the two stars in it, the distance between them is r and the distance around the center of mass is

       r’= r / 2

       G M² / r² = M v² / (r / 2)

       G M / r = 2 v²

The linear velocity module is constant, so we can use the kinematic relationship

       v = d / t

The distance of a circle of radius r ’is

      d = 2π r ’= 2π (r / 2)

      d = π r

We replace

      v = π r / T

Let's write the two equations

      v² = ½ G M / r

      v = π r / T

      r = v T /π

      v² = ½ G M π/ vT

      M = 2 v³ T / π G

Let's reduce the magnitudes to the SI system

     v = 160 Km / s = 1.60 10⁵ m / s

     T = 13.7 days (24 h / 1 day) (3600s / 1 h) = 1.18 10⁶ s

Let's calculate

     M = 2 (1.60 10⁵)³ 1.18 10⁶ / (π 6.67 10⁻¹¹)

     M = 4.61 10³¹ kg

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles